scholarly journals Bayesian mechanics for stationary processes

2021 ◽  
Vol 477 (2256) ◽  
Author(s):  
Lancelot Da Costa ◽  
Karl Friston ◽  
Conor Heins ◽  
Grigorios A. Pavliotis
Keyword(s):  
Steady State ◽  
Pid Control ◽  
Adaptive Systems ◽  
Theoretical Biology ◽  
Variational Inference ◽  
Adaptive Behaviour ◽  
Stationary Processes ◽  
Active Inference ◽  
Internal States ◽  
Markov Blankets

This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the interface between a system and its environment with a Markov blanket. This affords conditions under which states internal to the blanket encode information about external states. Second, we introduce dynamics and represent adaptive systems as Markov blankets at steady state. This allows us to identify a wide class of systems whose internal states appear to infer external states, consistent with variational inference in Bayesian statistics and theoretical neuroscience. Finally, we partition the blanket into sensory and active states. It follows that active states can be seen as performing active inference and well-known forms of stochastic control (such as PID control), which are prominent formulations of adaptive behaviour in theoretical biology and engineering.

Earth system resilience through planetary active inference.

2021 ◽  
Author(s):  
Sergio Rubin ◽  
Lancelot Da Costa ◽  
Karl Friston
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Solar Radiation ◽  
Royal Society ◽  
Metabolic Rates ◽  
Earth System ◽  
Active Inference ◽  
The Earth ◽  
Internal States ◽  
Markov Blankets

<p><strong>We formalize the resilience of the Earth system under the free energy principle (Friston 2013; Parr et al, 2019; Rubin et al, 2020). This allows us to understand resilience as the self-maintenance of a non-equilibrium steady-state. This autopoietic steady-state depends on gradient flows that counter entropic dissipation by random fluctuations. These flows can also be interpreted in a statistical sense, which amounts to the claim that resilience depends upon the Earth system possessing a Markov blanket were blanket states (i.e., active and sensory states) separate internal states from external states. Our formalization rests on how the metabolic rates of the biosphere (i.e., internal states) relate vicariously to solar radiation at the Earth’s surface (i.e., external states), through the changes in greenhouse and albedo effects (i.e. active states) and ocean-driven global temperature changes (i.e. sensory states). Describing the interaction between the metabolic rates and solar radiation as climatic states—via a Markov blanket—amounts to describing the dynamics of the internal states as actively inferring external states. This underwrites climatic non-equilibrium steady-state through variational free energy minimization—and thus a form of Earth resilience, through active inference at the planetary scale.</strong></p><p><strong>References</strong></p><p>Friston, K., 2013. Life as we know it. Journal of the Royal Society Interface, 10(86), p.20130475.</p><p>Parr, T., Da Costa, L. and Friston, K., 2019. Markov blankets, information geometry and stochastic thermodynamics. <em>Philosophical Transactions of the Royal Society A</em>, <em>378</em>(2164), p.20190159.</p><p>Rubin, S., Parr, T., Da Costa, L. and Friston, K., 2020. Future climates: Markov blankets and active inference in the biosphere. <em>Journal of the Royal Society Interface</em>, 17(172), p.20200503.</p>

scholarly journals Stochastic Chaos and Markov Blankets

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1220
Author(s):  
Karl Friston ◽  
Conor Heins ◽  
Kai Ueltzhöffer ◽  
Lancelot Da Da Costa ◽  
Thomas Parr
Keyword(s):  
Steady State ◽  
Functional Form ◽  
Lorenz System ◽  
State Density ◽  
Mathematical Basis ◽  
Stochastic Chaos ◽  
Internal States ◽  
The Lorenz System ◽  
Polynomial Expansions ◽  
Markov Blankets

In this treatment of random dynamical systems, we consider the existence—and identification—of conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions has interesting implications for the information geometry of internal states. In brief, this geometry can be read as a physics of sentience, where internal states look as if they are inferring external states. However, the existence of such partitions—and the functional form of the underlying densities—have yet to be established. Here, using the Lorenz system as the basis of stochastic chaos, we leverage the Helmholtz decomposition—and polynomial expansions—to parameterise the steady-state density in terms of surprisal or self-information. We then show how Markov blankets can be identified—using the accompanying Hessian—to characterise the coupling between internal and external states in terms of a generalised synchrony or synchronisation of chaos. We conclude by suggesting that this kind of synchronisation may provide a mathematical basis for an elemental form of (autonomous or active) sentience in biology.

scholarly journals Future climates: Markov blankets and active inference in the biosphere

2020 ◽  
Vol 17 (172) ◽  
pp. 20200503 ◽  
Author(s):  
Sergio Rubin ◽  
Thomas Parr ◽  
Lancelot Da Costa ◽  
Karl Friston
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Solar Radiation ◽  
Theoretical Biology ◽  
Metabolic Rates ◽  
Markov Blanket ◽  
Gaia Hypothesis ◽  
The Earth ◽  
Internal States ◽  
Non Equilibrium

We formalize the Gaia hypothesis about the Earth climate system using advances in theoretical biology based on the minimization of variational free energy. This amounts to the claim that non-equilibrium steady-state dynamics—that underwrite our climate—depend on the Earth system possessing a Markov blanket. Our formalization rests on how the metabolic rates of the biosphere (understood as Markov blanket's internal states) change with respect to solar radiation at the Earth's surface (i.e. external states), through the changes in greenhouse and albedo effects (i.e. active states) and ocean-driven global temperature changes (i.e. sensory states). Describing the interaction between the metabolic rates and solar radiation as climatic states—in a Markov blanket—amounts to describing the dynamics of the internal states as actively inferring external states. This underwrites climatic non-equilibrium steady-state through free energy minimization and thus a form of planetary autopoiesis.

scholarly journals The Natural Medium as Carrier of Meanings and Their Decoding by Living Beings: Biosemiotics in Action

2018 ◽  
Vol 23 (2) ◽  
pp. 192-218
Author(s):  
Helena Knyazeva
Keyword(s):  
Cognitive Science ◽  
Complex Adaptive Systems ◽  
Adaptive Systems ◽  
Theoretical Biology ◽  
Living Organism ◽  
Cognitive Agent ◽  
Life Activity ◽  
Autopoietic System ◽  
Complex Adaptive ◽  
Von Uexküll

The synthetic, integrative significance of biosemiotics as a modern interdisciplinary research program is under discussion in the article. Aimed at studying the cognitive and life activity of living beings, which are capable of recognizing signals and extracting the meanings, biosemiotics serves as a conceptual node that combines some important notions of theoretical biology, evolutionary epistemology, cognitive science, phenomenology, neuroscience and neurophilosophy as well as the theory of complex adaptive systems and network science. Worlds of perception and actions of living beings are built in the process of co-evolution, in structural coupling and in enactive interaction with the surrounding natural environment (Umwelt). Thereby the biosemiotic theories developed by the founders of biosemiotics (J. von Uexküll, Th. Sebeok, G. Prodi, H. Pattie) are conceptually closed to the system-structural evolutionary approach developed in synergetics by H. Haken and S.P. Kurdyumov, the conception of autopoiesis (H. Maturana and F. Varela), second-order cybernetics (H. von Foerster), the conception of enactivism in cognitive science (F. Varela, E. Thompson, A. Noë). The key to comprehending the processes of extracting and generating meanings is that every living organism lives in the subjectively built world (Umwelt), so that its Umwelt and its internal psychic organization become parts of a single autopoietic system. According to the well-known expression of G. Bateson, information is a not indifferent difference or a difference that makes a difference. Differences become information when a cognitive agent as an interpreter, acting as part of an autopoietic system, sees signs in these differences that make meanings.

scholarly journals Active Inferants: An Active Inference Framework for Ant Colony Behavior

2021 ◽  
Vol 15 ◽  
Author(s):  
Daniel Ari Friedman ◽  
Alec Tschantz ◽  
Maxwell J. D. Ramstead ◽  
Karl Friston ◽  
Axel Constant
Keyword(s):  
Theoretical Biology ◽  
Behavioral Model ◽  
Ant Colony ◽  
Behavioral Modeling ◽  
Multiscale Approach ◽  
Active Inference ◽  
Behavioral Experiments ◽  
Case System ◽  
Markov Decision ◽  
Trail Formation

In this paper, we introduce an active inference model of ant colony foraging behavior, and implement the model in a series of in silico experiments. Active inference is a multiscale approach to behavioral modeling that is being applied across settings in theoretical biology and ethology. The ant colony is a classic case system in the function of distributed systems in terms of stigmergic decision-making and information sharing. Here we specify and simulate a Markov decision process (MDP) model for ant colony foraging. We investigate a well-known paradigm from laboratory ant colony behavioral experiments, the alternating T-maze paradigm, to illustrate the ability of the model to recover basic colony phenomena such as trail formation after food location discovery. We conclude by outlining how the active inference ant colony foraging behavioral model can be extended and situated within a nested multiscale framework and systems approaches to biology more generally.

scholarly journals A new adaptive PSO-PID control strategy of hybrid energy storage system for electric vehicles

2020 ◽  
Vol 12 (9) ◽  
pp. 168781402095857
Author(s):  
Kanglong Ye ◽  
Peiqing Li
Keyword(s):  
Steady State ◽  
Control Strategy ◽  
Pid Control ◽  
Pid Controller ◽  
Storage System ◽  
Pso Algorithm ◽  
Energy Storage System ◽  
Hybrid Energy ◽  
Hybrid Energy Storage ◽  
Hybrid Energy Storage System

Research on optimization of control strategy for hybrid energy storage system (HESS) of the electric vehicle (EV), a new adaptive control strategy based on particle swarm optimization (PSO) algorithm is proposed in this paper. The steady-state power of the filtered power is used as the ideal output power of the battery. For the steady-state current output of the battery, the output power of the ultracapacitor is dynamically adjusted by the proportional-integral-derivative (PID) controller to construct a power difference control structure. The parameters of PID controller are optimized by PSO algorithm, and the target test is compared and analyzed based on MATLAB/Advisor. The research results show that the proposed PSO-PID control strategy can quickly eliminate the power deviation and achieve the approximate global optimization of the EV energy management strategy. Compared with the pre-optimized PID control strategy, the output current and power of the battery pack are smoother and the total power consumption is reduced by 3.8360% and 0.5125%, respectively. Then, the energy consumption parameters of PSO-PID are compared with the theoretical minimum energy consumption calculated by dynamic programming (DP) algorithm, and the deviation is less than 1% under both conditions.

scholarly journals Is the Free-Energy Principle a Formal Theory of Semantics? From Variational Density Dynamics to Neural and Phenotypic Representations

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 889 ◽  
Author(s):  
Maxwell J. D. Ramstead ◽  
Karl J. Friston ◽  
Inês Hipólito
Keyword(s):  
Free Energy ◽  
Formal Semantics ◽  
Formal Theory ◽  
Semantic Content ◽  
Active Inference ◽  
Explanatory Role ◽  
Energy Principle ◽  
Free Energy Principle ◽  
Neural Representations ◽  
Internal States

The aim of this paper is twofold: (1) to assess whether the construct of neural representations plays an explanatory role under the variational free-energy principle and its corollary process theory, active inference; and (2) if so, to assess which philosophical stance—in relation to the ontological and epistemological status of representations—is most appropriate. We focus on non-realist (deflationary and fictionalist-instrumentalist) approaches. We consider a deflationary account of mental representation, according to which the explanatorily relevant contents of neural representations are mathematical, rather than cognitive, and a fictionalist or instrumentalist account, according to which representations are scientifically useful fictions that serve explanatory (and other) aims. After reviewing the free-energy principle and active inference, we argue that the model of adaptive phenotypes under the free-energy principle can be used to furnish a formal semantics, enabling us to assign semantic content to specific phenotypic states (the internal states of a Markovian system that exists far from equilibrium). We propose a modified fictionalist account—an organism-centered fictionalism or instrumentalism. We argue that, under the free-energy principle, pursuing even a deflationary account of the content of neural representations licenses the appeal to the kind of semantic content involved in the ‘aboutness’ or intentionality of cognitive systems; our position is thus coherent with, but rests on distinct assumptions from, the realist position. We argue that the free-energy principle thereby explains the aboutness or intentionality in living systems and hence their capacity to parse their sensory stream using an ontology or set of semantic factors.

Switching-Type Self-Tuning Fuzzy PID Control of an Active Magnetic Bearing System

2013 ◽  
Vol 284-287 ◽  
pp. 2330-2336
Author(s):  
Kuan Yu Chen ◽  
Pi Cheng Tung ◽  
Yi Hua Fan
Keyword(s):  
Steady State ◽  
Transient Response ◽  
Pid Control ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
The Other ◽  
Fuzzy Pid ◽  
Switching Type ◽  
Self Tuning ◽  
Amb System

This paper presents a new switching control scheme for an active magnetic bearing (AMB) system using self-tuning fuzzy proportional-integral-derivative (PID) control. The research process consists of three stages. First, four types of self-tuning fuzzy PID-type controllers (FPIDCs) consisting of two most commonly used fuzzy inference systems: Mamdani and Takagi-Sugeno types, and two efficient parameter adaptive methods: function tuner and relative rate observer, are used to control a highly nonlinear AMB system, respectively. Hence, there are two kinds of FPIDCs can be obtained by comparing experimental results of these tests: one has the fastest transient response and the other has the minimum steady-state error. Next, the switching-type self-tuning FPIDC is proposed by combining the two kinds of FPIDCs. Namely, the AMB system is dominated by the scheme with the fastest transient response when the rotor is at rest and by the one with the best steady-state performance when the rotor is in rotation. Finally, experimental results demonstrate that the proposed switching-type self-tuning FPIDC performs better overall performance than the other self-tuning FPIDCs, particularly when controlling an AMB system.

scholarly journals An Active Inference Model of Collective Intelligence

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 830
Author(s):  
Rafael Kaufmann ◽  
Pranav Gupta ◽  
Jacob Taylor
Keyword(s):  
Theory Of Mind ◽  
Cognitive Ability ◽  
Complex Adaptive Systems ◽  
Adaptive Systems ◽  
Composite System ◽  
Collective Intelligence ◽  
Active Inference ◽  
Goal Alignment ◽  
Alignment Model ◽  
The Relationship

Collective intelligence, an emergent phenomenon in which a composite system of multiple interacting agents performs at levels greater than the sum of its parts, has long compelled research efforts in social and behavioral sciences. To date, however, formal models of collective intelligence have lacked a plausible mathematical description of the relationship between local-scale interactions between autonomous sub-system components (individuals) and global-scale behavior of the composite system (the collective). In this paper we use the Active Inference Formulation (AIF), a framework for explaining the behavior of any non-equilibrium steady state system at any scale, to posit a minimal agent-based model that simulates the relationship between local individual-level interaction and collective intelligence. We explore the effects of providing baseline AIF agents (Model 1) with specific cognitive capabilities: Theory of Mind (Model 2), Goal Alignment (Model 3), and Theory of Mind with Goal Alignment (Model 4). These stepwise transitions in sophistication of cognitive ability are motivated by the types of advancements plausibly required for an AIF agent to persist and flourish in an environment populated by other highly autonomous AIF agents, and have also recently been shown to map naturally to canonical steps in human cognitive ability. Illustrative results show that stepwise cognitive transitions increase system performance by providing complementary mechanisms for alignment between agents’ local and global optima. Alignment emerges endogenously from the dynamics of interacting AIF agents themselves, rather than being imposed exogenously by incentives to agents’ behaviors (contra existing computational models of collective intelligence) or top-down priors for collective behavior (contra existing multiscale simulations of AIF). These results shed light on the types of generic information-theoretic patterns conducive to collective intelligence in human and other complex adaptive systems.

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